https://telegra.ph/TON-DNS-auction-rules-07-21

In regards to price action, the following is copied from the link above:

Minimum price.
As protection against spamming bots that automatically register names, there will be a base price and floor price one has to pay.

The base price and floor price depend on the number of characters in your domain name.

Base price — The price at which begins the bidding.

Floor price — A price that cannot go lower than this threshold.

Number of characters: Base price/floor price.

4 characters: 1,000/100 Toncoin

5 characters: 500/50 Toncoin

6 characters: 400/40 Toncoin

7 characters: 300/30 Toncoin

8 characters: 200/20 Toncoin

9 characters: 100/10 Toncoin

10 characters: 50/5 Toncoin

More than 11 characters: 10/1 Toncoin

Every 30 days, the current base price will decrease by 10% until it reaches the floor price.